At the finer scale of individual migrating birds, migration speed is closely linked to flight speed and/or stopover duration (rest, fuel) (Schmaljohann 2018). Translated to macroecological context, migration synchronicity can be associated with intrinsic species-specific factors as well as external factors like environmental and landscape features. The major internal factors possibly affecting synchronicity are species’ morphological traits (affecting flight speed capability, such as dispersal ability, body size?), migration distance (Winger et al. 2024), and urgency of migration (related to within- and across-season differences in programming of internal clocks). On the other hand, external factors refer to the biogeomorphology of migration routes and wintering ranges, which influences food availability, interspecific competition, etc. and therefore influences how conducive various latitudes are to the fitness of the birds.
There is evidence that the latter is more important (Lindström 2003; Nilsson et al. 2013; Schmaljohann 2018), even at the macroecological scale (La Sorte et al. 2016). That is, external factors influencing aspects of foraging/fuelling are more important than intrinsic morphological or programmed factors like Zugunruhe. In India, this might be especially true for species taking the northwest vs Himalayan migration routes. In terms of both food availability and competition, the arid northwest region of India might be very conducive during the post-monsoon period (coinciding with arrival of winter migrants), due to the sudden burst in food availability coupled with lower competitive pressure due to lower local species richness. Thus, many species taking this route may spend longer coming down to reach the southern limit of their wintering range.
We test these multiple theories using our dataset, with the following predictions (simple illustrative graphs can be created later):
For high-res versions of images, go here.
After all our selection and filtering criteria for wintering species of interest (giving 90 species), and after filtering data for each species to its wintering latitudinal range (removing latitudes where not purely wintering), we now start the analysis.
Using quantiles (assuming 95%), we determine “true” arrival and departure dates for each species per latitude. For a preliminary visualisation of patterns across species, we visualise this latitudinal trend of arrival (blue) & departure (red) times for all species:
Figure 1: True arrival and departure timings of our wintering species, using the quantile method.
Figure 2: True arrival and departure timings of our wintering species, using the quantile method.
We now calculate metrics for migration timings, such as first northern/southern arrival & departure, and synchronicity which is our primary metric of interest. We describe synchronicity using two (presumably) orthogonal angles: slope (quickness of migration) and tightness (uniformity) across latitudes. (Correlation R2 cannot be used for the measure of tightness, since for high slope values, R2 becomes low.)
Here are the synchronicity measures (SYNC.SLOPE & SYNC.TIGHT) for a set of illustrative species, followed by updated plots for the same species.
## # A tibble: 50 × 6
## COMMON.NAME DATE.TYPE SLOPE SE SYNC.SLOPE SYNC.TIGHT
## <chr> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 Cinereous Vulture DEP 6.21 0.921 -1.60 0.0827
## 2 Bar-tailed Godwit DEP 3.89 2.60 -1.19 -0.956
## 3 Brown-breasted Flycatcher DEP 2.47 0.479 -0.795 0.737
## 4 Black Redstart DEP 2.21 0.292 -0.696 1.23
## 5 Blyth's Reed Warbler DEP 1.86 0.213 -0.548 1.55
## 6 Red-breasted Flycatcher DEP 1.53 0.312 -0.373 1.16
## 7 Lesser Whitethroat DEP 1.50 0.462 -0.361 0.771
## 8 Common Chiffchaff DEP 1.46 0.410 -0.332 0.891
## 9 Siberian Stonechat DEP 1.39 0.246 -0.293 1.40
## 10 Bar-headed Goose DEP 1.26 0.283 -0.203 1.26
## 11 Taiga Flycatcher DEP 0.988 0.300 0.00665 1.21
## 12 Eurasian Wigeon DEP 0.795 0.344 0.197 1.07
## 13 Brown-headed Gull DEP -0.766 0.472 0.229 0.750
## 14 Brown Shrike DEP 0.519 0.282 0.570 1.27
## 15 Tufted Duck DEP 0.511 0.447 0.584 0.806
## 16 Spotted Redshank DEP 0.504 0.327 0.595 1.12
## 17 Greenish Warbler DEP -0.459 0.362 0.677 1.02
## 18 Gray Wagtail DEP 0.425 0.253 0.745 1.38
## 19 Green Warbler DEP 0.363 0.467 0.883 0.762
## 20 Common Buzzard DEP -0.272 0.880 1.13 0.128
## 21 Greater Spotted Eagle DEP 0.245 0.254 1.23 1.37
## 22 Sykes's Warbler DEP 0.147 0.847 1.67 0.166
## 23 Western Yellow Wagtail DEP 0.0612 0.241 2.44 1.42
## 24 Booted Eagle DEP -0.0444 0.250 2.72 1.39
## 25 Pallid Harrier DEP 0.0227 0.334 3.31 1.10
## 26 Blyth's Reed Warbler ARR -3.33 0.459 -1.06 0.778
## 27 Cinereous Vulture ARR -2.39 2.38 -0.766 -0.866
## 28 Green Warbler ARR -1.78 0.270 -0.510 1.31
## 29 Brown-breasted Flycatcher ARR -1.78 1.02 -0.506 -0.0229
## 30 Western Yellow Wagtail ARR -1.73 0.204 -0.481 1.59
## 31 Pallid Harrier ARR -1.62 0.240 -0.423 1.43
## 32 Sykes's Warbler ARR -1.51 0.984 -0.362 0.0157
## 33 Eurasian Wigeon ARR -1.35 0.272 -0.266 1.30
## 34 Common Chiffchaff ARR -1.22 0.440 -0.176 0.821
## 35 Brown-headed Gull ARR -1.04 0.533 -0.0368 0.630
## 36 Bar-tailed Godwit ARR -0.997 0.958 -0.000733 0.0428
## 37 Greenish Warbler ARR -0.980 0.280 0.0143 1.27
## 38 Booted Eagle ARR -0.976 0.209 0.0177 1.57
## 39 Brown Shrike ARR -0.732 0.160 0.270 1.83
## 40 Taiga Flycatcher ARR -0.722 0.250 0.281 1.39
## 41 Siberian Stonechat ARR -0.705 0.182 0.302 1.70
## 42 Tufted Duck ARR -0.700 0.527 0.308 0.640
## 43 Red-breasted Flycatcher ARR -0.642 0.248 0.384 1.39
## 44 Lesser Whitethroat ARR -0.610 0.255 0.429 1.36
## 45 Spotted Redshank ARR 0.552 1.02 0.516 -0.0168
## 46 Common Buzzard ARR 0.480 0.335 0.637 1.09
## 47 Black Redstart ARR -0.409 0.172 0.779 1.76
## 48 Gray Wagtail ARR 0.342 0.209 0.934 1.57
## 49 Bar-headed Goose ARR -0.129 0.146 1.79 1.92
## 50 Greater Spotted Eagle ARR 0.0515 0.332 2.59 1.10
Figure 3: Set of illustrative species arranged in order of synchronicity of arrival/departure.
Figure 4: Set of illustrative species arranged in order of synchronicity of arrival/departure.
All our species can be visualised as occupying a 2-D space governed by the two measures of synchronicity. Based on their occupancy of this space, we can classify their overall synchronicity.
Figure 5: 2D space of synchronicity measures of our species.
Now will try to combine the two variables into a single index of synchronicity. Relative weights are obtained from PCA of the two variables, and the index (SYNC.IND) is a linear combination of the two. New values and updated graphs below.
## # A tibble: 50 × 5
## COMMON.NAME DATE.TYPE SYNC.SLOPE SYNC.TIGHT SYNC.IND
## <chr> <fct> <dbl> <dbl> <dbl>
## 1 Bar-tailed Godwit DEP -1.19 -0.956 -1.12
## 2 Cinereous Vulture DEP -1.60 0.0827 -1.08
## 3 Brown-breasted Flycatcher DEP -0.795 0.737 -0.320
## 4 Black Redstart DEP -0.696 1.23 -0.0982
## 5 Lesser Whitethroat DEP -0.361 0.771 -0.00962
## 6 Common Chiffchaff DEP -0.332 0.891 0.0472
## 7 Blyth's Reed Warbler DEP -0.548 1.55 0.102
## 8 Red-breasted Flycatcher DEP -0.373 1.16 0.103
## 9 Siberian Stonechat DEP -0.293 1.40 0.233
## 10 Bar-headed Goose DEP -0.203 1.26 0.252
## 11 Taiga Flycatcher DEP 0.00665 1.21 0.378
## 12 Brown-headed Gull DEP 0.229 0.750 0.391
## 13 Eurasian Wigeon DEP 0.197 1.07 0.466
## 14 Tufted Duck DEP 0.584 0.806 0.653
## 15 Spotted Redshank DEP 0.595 1.12 0.757
## 16 Greenish Warbler DEP 0.677 1.02 0.782
## 17 Brown Shrike DEP 0.570 1.27 0.786
## 18 Common Buzzard DEP 1.13 0.128 0.822
## 19 Green Warbler DEP 0.883 0.762 0.846
## 20 Gray Wagtail DEP 0.745 1.38 0.940
## 21 Sykes's Warbler DEP 1.67 0.166 1.21
## 22 Greater Spotted Eagle DEP 1.23 1.37 1.27
## 23 Western Yellow Wagtail DEP 2.44 1.42 2.13
## 24 Booted Eagle DEP 2.72 1.39 2.31
## 25 Pallid Harrier DEP 3.31 1.10 2.62
## 26 Cinereous Vulture ARR -0.766 -0.866 -0.797
## 27 Blyth's Reed Warbler ARR -1.06 0.778 -0.487
## 28 Brown-breasted Flycatcher ARR -0.506 -0.0229 -0.357
## 29 Sykes's Warbler ARR -0.362 0.0157 -0.245
## 30 Bar-tailed Godwit ARR -0.000733 0.0428 0.0127
## 31 Green Warbler ARR -0.510 1.31 0.0545
## 32 Common Chiffchaff ARR -0.176 0.821 0.133
## 33 Pallid Harrier ARR -0.423 1.43 0.151
## 34 Western Yellow Wagtail ARR -0.481 1.59 0.160
## 35 Brown-headed Gull ARR -0.0368 0.630 0.170
## 36 Eurasian Wigeon ARR -0.266 1.30 0.220
## 37 Spotted Redshank ARR 0.516 -0.0168 0.351
## 38 Greenish Warbler ARR 0.0143 1.27 0.405
## 39 Tufted Duck ARR 0.308 0.640 0.411
## 40 Booted Eagle ARR 0.0177 1.57 0.498
## 41 Taiga Flycatcher ARR 0.281 1.39 0.624
## 42 Red-breasted Flycatcher ARR 0.384 1.39 0.697
## 43 Lesser Whitethroat ARR 0.429 1.36 0.719
## 44 Siberian Stonechat ARR 0.302 1.70 0.736
## 45 Brown Shrike ARR 0.270 1.83 0.754
## 46 Common Buzzard ARR 0.637 1.09 0.779
## 47 Black Redstart ARR 0.779 1.76 1.08
## 48 Gray Wagtail ARR 0.934 1.57 1.13
## 49 Bar-headed Goose ARR 1.79 1.92 1.83
## 50 Greater Spotted Eagle ARR 2.59 1.10 2.13
Figure 6: Species arranged in order of combination of two synchronicity measures.
Figure 7: Species arranged in order of combination of two synchronicity measures.
Clearly, there is still some finetuning to be done with the “quickness” metric, i.e., derived from slope. For the most synchronous species with little difference between them, the values are drastically different. Also need to figure out how to appropriately weight the two so that high togetherness is prioritised.
Further try ordinations to understand what factors (wintering, migrating) determine synchronicity of species.
On discussing with AV, we realised that the second aspect, “tightness” is better viewed as noise rather than information. Even if it appears to have ecological meaning, this is only true for high tightness values and here the information is mostly just from the first metric. So, instead of trying to combine the two aspects, better to ignore species with tightness lower than some threshold value. Consider that low tightness can either be just noise in data, or lack of a strong north-south migration signal in the species, and we can’t tease apart the two (and not of interest in this study; though might still be an orthogonal aspect of synchronicity). So, changes applied:
## # A tibble: 5 × 8
## COMMON.NAME DATE.TYPE LM.SLOPE LM.SE SCALED.LM.SLOPE SCALED.LM.SE GLM.SLOPE GLM.SE
## <chr> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Black-capped Kingfisher ARR -2.11 2.87 -2.11 2.87 0.979 1.01
## 2 Black-naped Oriole ARR 2.78 1.47 2.78 1.47 1.03 1.00
## 3 Black-throated Thrush ARR -3.67 1.39 -3.67 1.39 0.876 1.03
## 4 Common Pochard ARR 0.0714 1.06 0.0714 1.06 1.00 1.00
## 5 Eurasian Griffon ARR -0.514 2.05 -0.514 2.05 0.942 1.08
Arranging in order of new synchronicity index (slope of LM):
## # A tibble: 50 × 4
## COMMON.NAME DATE.TYPE SYNC.IND SE
## <chr> <fct> <dbl> <dbl>
## 1 Brown-headed Gull DEP -0.766 0.472
## 2 Greenish Warbler DEP -0.459 0.362
## 3 Common Buzzard DEP -0.272 0.880
## 4 Booted Eagle DEP -0.0444 0.250
## 5 Pallid Harrier DEP 0.0227 0.334
## 6 Western Yellow Wagtail DEP 0.0612 0.241
## 7 Sykes's Warbler DEP 0.147 0.847
## 8 Greater Spotted Eagle DEP 0.245 0.254
## 9 Green Warbler DEP 0.363 0.467
## 10 Gray Wagtail DEP 0.425 0.253
## 11 Spotted Redshank DEP 0.504 0.327
## 12 Tufted Duck DEP 0.511 0.447
## 13 Brown Shrike DEP 0.519 0.282
## 14 Eurasian Wigeon DEP 0.795 0.344
## 15 Taiga Flycatcher DEP 0.988 0.300
## 16 Bar-headed Goose DEP 1.26 0.283
## 17 Siberian Stonechat DEP 1.39 0.246
## 18 Common Chiffchaff DEP 1.46 0.410
## 19 Lesser Whitethroat DEP 1.50 0.462
## 20 Red-breasted Flycatcher DEP 1.53 0.312
## 21 Blyth's Reed Warbler DEP 1.86 0.213
## 22 Black Redstart DEP 2.21 0.292
## 23 Brown-breasted Flycatcher DEP 2.47 0.479
## 24 Bar-tailed Godwit DEP 3.89 2.60
## 25 Cinereous Vulture DEP 6.21 0.921
## 26 Blyth's Reed Warbler ARR -3.33 0.459
## 27 Cinereous Vulture ARR -2.39 2.38
## 28 Green Warbler ARR -1.78 0.270
## 29 Brown-breasted Flycatcher ARR -1.78 1.02
## 30 Western Yellow Wagtail ARR -1.73 0.204
## 31 Pallid Harrier ARR -1.62 0.240
## 32 Sykes's Warbler ARR -1.51 0.984
## 33 Eurasian Wigeon ARR -1.35 0.272
## 34 Common Chiffchaff ARR -1.22 0.440
## 35 Brown-headed Gull ARR -1.04 0.533
## 36 Bar-tailed Godwit ARR -0.997 0.958
## 37 Greenish Warbler ARR -0.980 0.280
## 38 Booted Eagle ARR -0.976 0.209
## 39 Brown Shrike ARR -0.732 0.160
## 40 Taiga Flycatcher ARR -0.722 0.250
## 41 Siberian Stonechat ARR -0.705 0.182
## 42 Tufted Duck ARR -0.700 0.527
## 43 Red-breasted Flycatcher ARR -0.642 0.248
## 44 Lesser Whitethroat ARR -0.610 0.255
## 45 Black Redstart ARR -0.409 0.172
## 46 Bar-headed Goose ARR -0.129 0.146
## 47 Greater Spotted Eagle ARR 0.0515 0.332
## 48 Gray Wagtail ARR 0.342 0.209
## 49 Common Buzzard ARR 0.480 0.335
## 50 Spotted Redshank ARR 0.552 1.02
Figure 8: Species arranged in order of synchronicity (slope).
Figure 9: Species arranged in order of synchronicity (slope).
This is not very straightforward. Here is a summary of some select species and various measures of theirs (R-squared, residual standard error, degrees of freedom, F statistic, root mean square error, mean absolute error, coefficient of variation).
## # A tibble: 50 × 11
## COMMON.NAME DATE.TYPE SLOPE SE R2 RSE DF F.STAT RMSE MAE CV
## <chr> <fct> <dbl> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Brown-headed Gull DEP -0.766 0.472 0.141 13.2 16 2.63 12.5 9.69 1.32
## 2 Greenish Warbler DEP -0.459 0.362 0.0745 10.8 20 1.61 10.3 8.83 1.19
## 3 Common Buzzard DEP -0.272 0.880 0.00679 21.2 14 0.0958 19.9 14.1 1.45
## 4 Booted Eagle DEP -0.0444 0.250 0.00174 6.45 18 0.0314 6.12 4.95 1.27
## 5 Pallid Harrier DEP 0.0227 0.334 0.000256 8.96 18 0.00460 8.50 7.00 1.25
## 6 Western Yellow Wagtail DEP 0.0612 0.241 0.00293 8.50 22 0.0646 8.14 6.13 1.36
## 7 Sykes's Warbler DEP 0.147 0.847 0.00200 18.5 15 0.0301 17.3 13.1 1.37
## 8 Greater Spotted Eagle DEP 0.245 0.254 0.0387 9.16 23 0.927 8.79 6.80 1.32
## 9 Green Warbler DEP 0.363 0.467 0.0387 9.43 15 0.604 8.86 7.02 1.30
## 10 Gray Wagtail DEP 0.425 0.253 0.136 6.52 18 2.82 6.18 5.05 1.26
## 11 Spotted Redshank DEP 0.504 0.327 0.116 9.96 18 2.37 9.45 7.35 1.32
## 12 Tufted Duck DEP 0.511 0.447 0.0913 7.48 13 1.31 6.96 6.28 1.15
## 13 Brown Shrike DEP 0.519 0.282 0.134 9.55 22 3.40 9.14 6.49 1.44
## 14 Eurasian Wigeon DEP 0.795 0.344 0.195 12.4 22 5.33 11.9 8.88 1.37
## 15 Taiga Flycatcher DEP 0.988 0.300 0.364 8.31 19 10.9 7.91 5.59 1.45
## 16 Bar-headed Goose DEP 1.26 0.283 0.473 9.58 22 19.7 9.17 7.31 1.28
## 17 Siberian Stonechat DEP 1.39 0.246 0.667 5.86 16 32.1 5.52 4.50 1.26
## 18 Common Chiffchaff DEP 1.46 0.410 0.457 8.28 15 12.6 7.78 6.10 1.31
## 19 Lesser Whitethroat DEP 1.50 0.462 0.335 14.7 21 10.6 14.1 10.9 1.31
## 20 Red-breasted Flycatcher DEP 1.53 0.312 0.545 9.28 20 23.9 8.85 6.69 1.36
## 21 Blyth's Reed Warbler DEP 1.86 0.213 0.778 7.21 22 77.0 6.90 5.77 1.22
## 22 Black Redstart DEP 2.21 0.292 0.782 6.72 16 57.3 6.34 5.27 1.24
## 23 Brown-breasted Flycatcher DEP 2.47 0.479 0.708 7.30 11 26.7 6.72 5.03 1.39
## 24 Bar-tailed Godwit DEP 3.89 2.60 0.271 22.6 6 2.24 19.6 14.7 1.42
## 25 Cinereous Vulture DEP 6.21 0.921 0.835 10.5 9 45.5 9.48 8.07 1.23
## 26 Blyth's Reed Warbler ARR -3.33 0.459 0.705 15.6 22 52.5 14.9 11.0 1.39
## 27 Cinereous Vulture ARR -2.39 2.38 0.101 27.1 9 1.01 24.5 17.6 1.46
## 28 Green Warbler ARR -1.78 0.270 0.745 5.44 15 43.8 5.11 3.92 1.34
## 29 Brown-breasted Flycatcher ARR -1.78 1.02 0.215 15.6 11 3.02 14.4 8.60 1.74
## 30 Western Yellow Wagtail ARR -1.73 0.204 0.765 7.22 22 71.5 6.91 5.48 1.29
## 31 Pallid Harrier ARR -1.62 0.240 0.716 6.43 18 45.3 6.10 5.03 1.24
## 32 Sykes's Warbler ARR -1.51 0.984 0.135 21.5 15 2.34 20.2 17.3 1.20
## 33 Eurasian Wigeon ARR -1.35 0.272 0.527 9.81 22 24.5 9.39 7.30 1.31
## 34 Common Chiffchaff ARR -1.22 0.440 0.338 8.88 15 7.67 8.34 6.35 1.36
## 35 Brown-headed Gull ARR -1.04 0.533 0.192 14.9 16 3.80 14.1 10.6 1.36
## 36 Bar-tailed Godwit ARR -0.997 0.958 0.153 8.33 6 1.08 7.21 5.37 1.43
## 37 Greenish Warbler ARR -0.980 0.280 0.380 8.32 20 12.3 7.94 6.29 1.29
## 38 Booted Eagle ARR -0.976 0.209 0.548 5.38 18 21.9 5.11 3.69 1.42
## 39 Brown Shrike ARR -0.732 0.160 0.488 5.42 22 21.0 5.19 3.77 1.41
## 40 Taiga Flycatcher ARR -0.722 0.250 0.305 6.93 19 8.35 6.60 5.46 1.24
## 41 Siberian Stonechat ARR -0.705 0.182 0.483 4.35 16 14.9 4.10 3.04 1.39
## 42 Tufted Duck ARR -0.700 0.527 0.119 8.82 13 1.76 8.21 6.67 1.27
## 43 Red-breasted Flycatcher ARR -0.642 0.248 0.250 7.39 20 6.68 7.05 6.05 1.19
## 44 Lesser Whitethroat ARR -0.610 0.255 0.213 8.13 21 5.70 7.76 6.39 1.24
## 45 Black Redstart ARR -0.409 0.172 0.261 3.96 16 5.65 3.74 2.90 1.32
## 46 Bar-headed Goose ARR -0.129 0.146 0.0341 4.95 22 0.777 4.74 3.83 1.26
## 47 Greater Spotted Eagle ARR 0.0515 0.332 0.00104 12.0 23 0.0240 11.5 8.01 1.47
## 48 Gray Wagtail ARR 0.342 0.209 0.130 5.38 18 2.69 5.10 4.07 1.29
## 49 Common Buzzard ARR 0.480 0.335 0.128 8.08 14 2.06 7.56 5.58 1.40
## 50 Spotted Redshank ARR 0.552 1.02 0.0161 30.9 18 0.294 29.4 22.4 1.34
RMSE, MAE, and RSE make the most sense. Using thresholds of 20, 20, and 25 respectively, here is a summary of our example species that passed or failed wrt ARRIVAL timings.
## # A tibble: 25 × 9
## COMMON.NAME SLOPE SE RSE RMSE MAE RSE.PASS RMSE.PASS MAE.PASS
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <lgl> <lgl> <lgl>
## 1 Bar-headed Goose -0.129 0.146 4.95 4.74 3.83 TRUE TRUE TRUE
## 2 Bar-tailed Godwit -0.997 0.958 8.33 7.21 5.37 TRUE TRUE TRUE
## 3 Black Redstart -0.409 0.172 3.96 3.74 2.90 TRUE TRUE TRUE
## 4 Blyth's Reed Warbler -3.33 0.459 15.6 14.9 11.0 TRUE TRUE TRUE
## 5 Booted Eagle -0.976 0.209 5.38 5.11 3.69 TRUE TRUE TRUE
## 6 Brown Shrike -0.732 0.160 5.42 5.19 3.77 TRUE TRUE TRUE
## 7 Brown-breasted Flycatcher -1.78 1.02 15.6 14.4 8.60 TRUE TRUE TRUE
## 8 Brown-headed Gull -1.04 0.533 14.9 14.1 10.6 TRUE TRUE TRUE
## 9 Cinereous Vulture -2.39 2.38 27.1 24.5 17.6 FALSE FALSE TRUE
## 10 Common Buzzard 0.480 0.335 8.08 7.56 5.58 TRUE TRUE TRUE
## 11 Common Chiffchaff -1.22 0.440 8.88 8.34 6.35 TRUE TRUE TRUE
## 12 Eurasian Wigeon -1.35 0.272 9.81 9.39 7.30 TRUE TRUE TRUE
## 13 Gray Wagtail 0.342 0.209 5.38 5.10 4.07 TRUE TRUE TRUE
## 14 Greater Spotted Eagle 0.0515 0.332 12.0 11.5 8.01 TRUE TRUE TRUE
## 15 Green Warbler -1.78 0.270 5.44 5.11 3.92 TRUE TRUE TRUE
## 16 Greenish Warbler -0.980 0.280 8.32 7.94 6.29 TRUE TRUE TRUE
## 17 Lesser Whitethroat -0.610 0.255 8.13 7.76 6.39 TRUE TRUE TRUE
## 18 Pallid Harrier -1.62 0.240 6.43 6.10 5.03 TRUE TRUE TRUE
## 19 Red-breasted Flycatcher -0.642 0.248 7.39 7.05 6.05 TRUE TRUE TRUE
## 20 Siberian Stonechat -0.705 0.182 4.35 4.10 3.04 TRUE TRUE TRUE
## 21 Spotted Redshank 0.552 1.02 30.9 29.4 22.4 FALSE FALSE FALSE
## 22 Sykes's Warbler -1.51 0.984 21.5 20.2 17.3 TRUE FALSE TRUE
## 23 Taiga Flycatcher -0.722 0.250 6.93 6.60 5.46 TRUE TRUE TRUE
## 24 Tufted Duck -0.700 0.527 8.82 8.21 6.67 TRUE TRUE TRUE
## 25 Western Yellow Wagtail -1.73 0.204 7.22 6.91 5.48 TRUE TRUE TRUE
Figure 10: Comparisons of different measures of variability for arrival timings.
It is evident that RMSE is the most susceptible to single, large-deviance points pulling away the overall measure. It also seems that MAE might be the most appropriate for us: aside from Dunlin and Pied Harrier (which are treated similarly by all three), all other remove species have been clustered tightly and separated from the species we want to retain.
Let us check whether this is true for departure timings as well. Here, the best thresholds are 14, 10 and 15 respectively for RMSE, MAE and RSE.
## # A tibble: 25 × 9
## COMMON.NAME SLOPE SE RSE RMSE MAE RSE.PASS RMSE.PASS MAE.PASS
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <lgl> <lgl> <lgl>
## 1 Bar-headed Goose 1.26 0.283 9.58 9.17 7.31 TRUE TRUE TRUE
## 2 Bar-tailed Godwit 3.89 2.60 22.6 19.6 14.7 FALSE FALSE FALSE
## 3 Black Redstart 2.21 0.292 6.72 6.34 5.27 TRUE TRUE TRUE
## 4 Blyth's Reed Warbler 1.86 0.213 7.21 6.90 5.77 TRUE TRUE TRUE
## 5 Booted Eagle -0.0444 0.250 6.45 6.12 4.95 TRUE TRUE TRUE
## 6 Brown Shrike 0.519 0.282 9.55 9.14 6.49 TRUE TRUE TRUE
## 7 Brown-breasted Flycatcher 2.47 0.479 7.30 6.72 5.03 TRUE TRUE TRUE
## 8 Brown-headed Gull -0.766 0.472 13.2 12.5 9.69 TRUE TRUE TRUE
## 9 Cinereous Vulture 6.21 0.921 10.5 9.48 8.07 TRUE TRUE TRUE
## 10 Common Buzzard -0.272 0.880 21.2 19.9 14.1 FALSE FALSE FALSE
## 11 Common Chiffchaff 1.46 0.410 8.28 7.78 6.10 TRUE TRUE TRUE
## 12 Eurasian Wigeon 0.795 0.344 12.4 11.9 8.88 TRUE TRUE TRUE
## 13 Gray Wagtail 0.425 0.253 6.52 6.18 5.05 TRUE TRUE TRUE
## 14 Greater Spotted Eagle 0.245 0.254 9.16 8.79 6.80 TRUE TRUE TRUE
## 15 Green Warbler 0.363 0.467 9.43 8.86 7.02 TRUE TRUE TRUE
## 16 Greenish Warbler -0.459 0.362 10.8 10.3 8.83 TRUE TRUE TRUE
## 17 Lesser Whitethroat 1.50 0.462 14.7 14.1 10.9 TRUE FALSE FALSE
## 18 Pallid Harrier 0.0227 0.334 8.96 8.50 7.00 TRUE TRUE TRUE
## 19 Red-breasted Flycatcher 1.53 0.312 9.28 8.85 6.69 TRUE TRUE TRUE
## 20 Siberian Stonechat 1.39 0.246 5.86 5.52 4.50 TRUE TRUE TRUE
## 21 Spotted Redshank 0.504 0.327 9.96 9.45 7.35 TRUE TRUE TRUE
## 22 Sykes's Warbler 0.147 0.847 18.5 17.3 13.1 FALSE FALSE FALSE
## 23 Taiga Flycatcher 0.988 0.300 8.31 7.91 5.59 TRUE TRUE TRUE
## 24 Tufted Duck 0.511 0.447 7.48 6.96 6.28 TRUE TRUE TRUE
## 25 Western Yellow Wagtail 0.0612 0.241 8.50 8.14 6.13 TRUE TRUE TRUE
Figure 11: Comparisons of different measures of variability for departure timings.
RMSE seems like a poor option again. MAE is again decent, but this time RSE is also good. Need to see how values for species change with updated 2024 data.
The number of species that pass and fail each criterion are:
## # A tibble: 6 × 5
## DATE.TYPE CRITERION FAIL PASS PASS.PROP
## <fct> <chr> <int> <int> <dbl>
## 1 DEP MAE.PASS 35 55 0.611
## 2 DEP RMSE.PASS 26 64 0.711
## 3 DEP RSE.PASS 27 63 0.7
## 4 ARR MAE.PASS 7 83 0.922
## 5 ARR RMSE.PASS 12 78 0.867
## 6 ARR RSE.PASS 9 81 0.9